Implement a parametrization function for Pyramid (#1163)

* Add parametrization for Pyramid

* Add tests

* Fix tests

* Simplify code

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Co-authored-by: Júlio Hoffimann <julio.hoffimann@gmail.com>

src/geometries/polytopes/pyramid.jl

@@ -15,3 +15,13 @@ nvertices(::Type{<:Pyramid}) = 5
 
 Base.isapprox(p₁::Pyramid, p₂::Pyramid; atol=atol(lentype(p₁)), kwargs...) =
   all(isapprox(v₁, v₂; atol, kwargs...) for (v₁, v₂) in zip(p₁.vertices, p₂.vertices))
+
+function (pyramid::Pyramid)(u, v, w)
+  if (u < 0 || u > 1) || (v < 0 || v > 1) || (w < 0 || w > 1)
+    throw(DomainError((u, v, w), "pyramid(u, v, w) is not defined for u, v, w outside [0, 1]³."))
+  end
+  a, b, c, d, o = vertices(pyramid)
+  q = Quadrangle(a, b, c, d)
+  s = Segment(q(u, v), o)
+  s(w)
+end

test/polytopes.jl

@@ -939,6 +939,9 @@ end
   @test crs(p) <: Cartesian{NoDatum}
   @test Meshes.lentype(p) == ℳ
   @test volume(p) ≈ T(1 / 3) * u"m^3"
+  @test p(T(1), T(1), T(0)) == vertices(p)[3]
+  @test p(T(0), T(0), T(1)) == vertices(p)[5]
+  @test_throws DomainError p(T(0), T(0), T(1.5))
   m = boundary(p)
   @test m isa Mesh
   @test nelements(m) == 5